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Properties

Label 116610ba
Number of curves $2$
Conductor $116610$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("ba1")
 
E.isogeny_class()
 

Elliptic curves in class 116610ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
116610.ba2 116610ba1 \([1, 0, 1, 9291, 445486]\) \(108750551/167670\) \(-136773569990070\) \([3]\) \(404352\) \(1.3977\) \(\Gamma_0(N)\)-optimal
116610.ba1 116610ba2 \([1, 0, 1, -89574, -17706128]\) \(-97435188409/109503000\) \(-89324961141663000\) \([]\) \(1213056\) \(1.9471\)  

Rank

sage: E.rank()
 

The elliptic curves in class 116610ba have rank \(0\).

Complex multiplication

The elliptic curves in class 116610ba do not have complex multiplication.

Modular form 116610.2.a.ba

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} - q^{7} - q^{8} + q^{9} + q^{10} + q^{12} + q^{14} - q^{15} + q^{16} + 3 q^{17} - q^{18} - 7 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.